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Sprint projectOct 25, 2026

Directional Predictive Evidence for Collusion Auditing: A Pre-Registered, Sprint-Scale Test of the APTG-RL Design

Aravinth K · Team chinchoo

Submitted to AI Collusion Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.

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Report: Directional Predictive Evidence for Collusion Auditing: A Pre-Registered, Sprint-Scale Test of the APTG-RL Design

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Auditing multi-agent systems for collusion requires telling coordination apart from shared context, shared model tendencies and prompt-induced behaviour shifts. We test the APTG-RL design: a directional predictive-gain statistic between agents, a time-varying directed graph with temporal features, and a reinforcement-learning investigator that decides when to alert (its prompt-conditioned baseline is not exercised by the reported detectors). We build a three-seller repeated pricing game with four scripted collusion mechanisms, benign and shared-model negatives, and a seven-condition controlled design (C0–C6) of unilateral and common instruction perturbations, scripted collusion and benign policy shifts. Ten detectors, including the information-theoretic net-influence baseline, are compared on held-out episodes at thresholds fixed on validation negatives, under a pre-registered plan. A combined same-round-and-lagged directional gain beats symmetric mutual information (AUROC 0.839 vs. 0.755) but not lag-1 net influence (0.850); its strictly lagged part alone showed no clear advantage over symmetric MI (AUROC 0.704 vs. 0.755; difference inconclusive), and the parametric gain misses a parity-coded hidden channel that mutual information catches. The temporal-graph score did not help (0.740), and the RL investigator, which only rediscovered a “look at the first window” rule, bought lower delay and cost at lower recall. No statistically clear increase in false alarms was established under unilateral instruction perturbation, although small condition-level samples leave moderate increases possible. A small pilot with Claude Haiku 4.5 agents (720 decisions, 0 invalid) confirms that the perturbation shifts behaviour. This is simulator-only evidence at small scale; we report the nulls, the deviations we made, and the limits.

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  1. This is a notably disciplined piece of sprint work. I checked your repository: PREREG.md was committed before the detection runner and never edited, the deviations are logged, and the numbers in your tables match the committed results. That rigor is what makes your nulls worth reading, so put the PREREG.md commit hash and time in the paper itself. My main request is to apply your own decision rule plainly. The pre-registered H1 required the directional score to beat both symmetric MI and net influence on TPR, and Table 4 shows it is significantly worse than net influence. I would report H1 as not supported and retitle the paper around your most useful finding, which is that each dependence statistic covers a different set of mechanisms. Please also give H5 an explicit verdict with confidence intervals and list the planned secondary outcomes you did not run.

    For next steps, wire in the prompt-conditioned baseline with a pooled cross-episode estimator. That is the idea that separates APTG from prior work, and it is still untested. Then run the detectors on LLM agents over longer episodes, because your reassuring false-alarm result under unilateral steering rests on a scripted perturbation model. A union of net influence, symmetric MI and a nonparametric directional statistic would be a cheap, high-value experiment.

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Cite this project

@misc{k2026directional,
  title = {{Directional Predictive Evidence for Collusion Auditing: A Pre-Registered, Sprint-Scale Test of the APTG-RL Design}},
  author = {Aravinth K},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/directional-predictive-evidence-for-collusion-auditing-a-preregistered-sprintscale-test-of-the-aptgrl-design-7pdd}},
  url = {https://apartresearch.com/sprints/projects/directional-predictive-evidence-for-collusion-auditing-a-preregistered-sprintscale-test-of-the-aptgrl-design-7pdd}
}

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